A Statistical Model for Directional Relations Between Spatial Objects

Abstract

Directional relation, as a kind of spatial constraints, has been recognized as being an important means for spatial query, analysis and reasoning. Directional relation is conventionally concerned with two point objects. However, in spatial query and analysis, there is also a need of directional relations between point and line, point and area, line and line, line and area, and area and area. Therefore, conventional definition of direction needs to be extended to include line and area objects (i.e. the so-called extended objects). Existing models for directional relation of extended objects make use of approximate representations (e.g. minimum bounding rectangles) of the extended objects so as to produce some results with unrealistic impression. In this paper, a statistical model is presented. In this new model, (1) an extended spatial object is decomposed into small components; (2) the directional relation between extended spatial objects is then determined by the directions between these small components which form a distribution; and (3) two measures (i.e. range and median direction) are utilized to describe the statistical property of the distribution. This statistical model is based upon the (extended) spatial objects themselves, instead of their approximate representations. An experimental test has been carried out and the result indicates that the directional relations computed from this model is very close to those perceived by human beings.

A computational model for direction relations between spatial objects in GIS

“…As shown in Fig. 5(a), metric details based on the proposed model are more stable and accurate than the statistics model proposed by Deng and Li [17]. Fig.…”

“…These models are used to present direction relations qualitatively. Because focus of implementation in GIS is on query that is based on quantitative representation, metric-based model for spatial relations is proposed, such as Voronoi model [16] and statistical model [17]. It becomes complex that qualitative direction relations are separated into several partitions for description based on Voronoi model, even though there are advantages to describe direction relations between intertwined objects.…”

A splitting line model for directional relations

“…Deng and Li [5] proposed a statistical approach. They rasterize polygons A and B into small cells, compute the angle between the centroids of each pair of cells, and return the median angle.…”

Fuzzy Spatio-temporal Relations Analysis

“…When the relations are captured with the help of 1D Allen relations, the distance relations has the importance when the objects are disjoint. For the disjoint relations the distance relations can be estimated from the support of a fuzzy Allen histogram because directional relations are proportional to the visual rang of object [17]. This range is inversely proportional to the distance between the objects.i.e.…”